# Which action would prevent a fracture in the cyclist?

Let's say a cyclist hits a tree and fractures his arm. Which of the following would have likely prevented the fracture:

a) decrease in his velocity by factor of 2
b) decrease in his mass by factor of 2

What arguments can be used here to reason this (ex. momentum, energy, force)? Immediately when I rephrased the question in my head to what change would have reduced the damage the most and thought of force. However, I guess you could also use the kinetic energy argument. I'm a little confused as to what the correct way to approach this is. At any rate, shouldn't all arguments lead to the same conclusion?

Thanks.

From Newton's 2nd Law, F=ma. If you can increase the time it takes to change velocity, then the impact time increases resulting in lower acceleration, thus lower the force.
From momentum, p=mv. If you decrease velocity by a factor of 2 in one case, and decrease mass by a factor of 2 in another case, I believe you will get the same momentum in both cases, but a difference in impact time and kinetic energy.
For kinetic energy, an average person weighs about 70kg, and a normal bike speed is ~15mph(which converts to ~6.7m/s). The kinetic energy when the velocity is halved is much less than when the mass is halved. I hope this help

But can we assume we're actually increasing/decreasing impact time?

$$velocity=\frac{distance}{time}$$
Holding distance fixed, if we increase the velocity, then the impact time decreases. If we decrease the velocity, the impact time increases.

E = 1/2mv^2

The energy dissipated by the guys arm broke it. Which part of the energy equation has the biggest impact on the value of E?